Through the philosophers we hear of a totally different Aspasia of Miletus -- a woman who could have and probably did teach Socrates a thing or two.

Socrates

[3.14] "But what of the husbands who, as you say, have good wives, Socrates? Did they train them themselves?" "There's nothing like investigation. I will introduce Aspasia to you, and she will explain the whole matter to you with more knowledge than I possess. [3.15] I think that the wife who is a good partner in the household contributes just as much as her husband to its good; because the incomings for the most part are the result of the husband's of the husband's exertions, but the outgoings are controlled mostly by the wife's dispensation. If both do their part well,the estate is increased; if they act incompetently, it is diminished." - Xenophon Economics

Xenophon

Aspasia of Miletus may have modelled "INDUCTIO" (described by Cicero as "getting one's interlocutor to assent to a doubtful proposition that resembles the earlier one") for Socrates.

For example, as in Aeschines of Sphettos' dialogue, Socrates shows that Aspasia spoke with Xenophon's wife and Xenophon himself:

"Tell me, please, wife of Xenophon, if your neighbor had a better peice of jewelry than you, would you prefer hers or your own?"
"Hers," said the wife."So -- if she should have a dress or other feminine ornament more expensive than what you have, would you prefer hers or yours?"
Hers, naturally," said the wife."So now: what if that woman had a better husband than you? Would you prefer hers or your own?"
Here the woman blushed. Aspasia, however, began to interrogate Xenophon himself.
(frag 31 Dittmar = Cic. Inv. Rhet. 1.31.51 ff.)

Prisoner of History

p. 43-44.

In all, we know for certain depressingly little about Aspasia. Most of Plutarch's statements about Aspasia are couched in qualifiers like "PHASI" (they say). As Professor Henry says, "with few exceptions, most citations of Aspasia float in a Sargasso Sea of protoprosopography, subhistory, and subbiography."